Thousands of people from the Bahamas are trying to flee the devastation left by Hurricane Dorian. The question is whether the United States is going to welcome them. At first, the Trump administration said that they would accept anyone from the Bahamas, for humanitarian reasons. Then late yesterday the Department of Homeland Security added a hurdle, saying that those coming by boat would still need a visa. NPR's Joel Rose is covering this and joins us in studio. Hi, Joel.

JOEL ROSE, BYLINE: Hey, Rachel.

MARTIN: So this is confusing for us on this end, even more confusing for people in the Bahamas, and the stakes so much higher for them, clearly.

ROSE: Right. I mean, there are real mixed signals here. Acting Customs and Border Protection Commissioner Mark Morgan held a White House press briefing yesterday, and he told reporters this.

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MARK MORGAN: If your life is in jeopardy, and you're in the Bahamas, and you want to get to United States, you're going to be allowed to come to United States - right? - whether you have travel documents or not.

MARTIN: OK.

ROSE: But later President Trump told reporters that, quote, "everybody needs totally proper documentation," unquote, because immigration authorities need to be careful about who's coming into the country. And late last night the Department of Homeland Security put out new guidance - anyone arriving by air or sea has to have a valid passport. If you're flying into the U.S. from Freeport or Nassau, which is the Bahamas capital, you don't need a visa. But if you're arriving by boat, you are going to need a passport and a visa to get into the U.S.

MARTIN: Why? I mean, what's the administration's rationale here?

ROSE: Well, partly, this is following a longstanding policy for Bahamians, which says they can get into the U.S. without a visa as long as they go to the airport with a passport and documentation that they do not have a criminal record. But according to this latest guidance, that's not going to apply to residents who are coming by boat. Here's President Trump yesterday.

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PRESIDENT DONALD TRUMP: I don't want to allow people that weren't supposed to be in the Bahamas to come in to the United States, including some very bad people and some very bad gang members and some very, very bad drug dealers.

ROSE: U.S. officials say the embassy in Nassau is open for emergency visa appointments. But this is an extra step. It could mean possible delays for people who are in a desperate situation after the hurricane. And Florida's two Republican senators have asked the Trump administration to waive any visa requirements for residents of the Bahamas.

MARTIN: So just so I'm clear - the president is saying it's not necessarily about Bahamian; this is about people who were in the Bahamas, not on the up and up.

ROSE: That's what he said.

MARTIN: OK. So the thrust of the briefing yesterday was supposed to be about the southern border, the U.S.-Mexico border. The administration called it to announce that the number of migrants taken into U.S. custody at the border has declined for the third month in a row. Is that true, Joel?

ROSE: It is. The crossing numbers continue to go down. Just over 64,000 people were either apprehended by the Border Patrol or taken into custody at the ports of entry. That is a big reduction since May, when the total number peaked at more than 144,000. And the administration credits a lot of this drop to the efforts of Mexico. Under a deal that was signed in June, the Mexican government has sent National Guard troops to its borders, and Mexico has also agreed to allow tens of thousands of Central American asylum-seekers to stay in that country while they wait for their day in U.S. immigration court.

But U.S. officials say we are still facing an emergency at the border. I talked yesterday to the acting director of Immigration and Customs Enforcement, Matthew Albence. Here's what he said.

MATTHEW ALBENCE: There are still tens of thousands of people that are trying to enter our country illegally. That is a crisis. Our infrastructure has been overwhelmed as a result of what's occurred over the past year, and we're still trying to catch up. So while it's great results thus far, we're far from saying that - mission accomplished.

ROSE: The administration wants Mexico to do even more. Mexican officials are in Washington this week for a meeting with Vice President Pence about what's going to happen next.